Luo, Hong Steady state solution to atmospheric circulation equations with humidity effect. (English) Zbl 1308.86005 J. Appl. Math. 2012, Article ID 867310, 18 p. (2012). Summary: The steady state solution to atmospheric circulation equations with humidity effect is studied. A sufficient condition of existence of steady state solution to atmospheric circulation equations is obtained, and regularity of steady state solution is verified. Cited in 2 Documents MSC: 86A10 Meteorology and atmospheric physics 35Q86 PDEs in connection with geophysics 35A01 Existence problems for PDEs: global existence, local existence, non-existence PDF BibTeX XML Cite \textit{H. Luo}, J. Appl. Math. 2012, Article ID 867310, 18 p. (2012; Zbl 1308.86005) Full Text: DOI OpenURL References: [1] T. Ma and S. H. Wang, Phase Transition Dynamics in Nonlinear Sciences, Springer, New York, NY, USA, 2012. [2] T. Ma, Theories and Methods in Partial Differential Equations, Science Press, Beijing, China, 2011. [3] N.A. Phillips, “The general circulation of the atmosphere: a numerical experiment,” Quarterly Journal of the Royal Meteorological Society, vol. 82, pp. 123-164, 1956. [4] C.G. Rossby, “On the solution of problems of atmospheric motion by means of model experiment,” Monthly Weather Review, vol. 54, pp. 237-240, 1926. [5] J.-L. Lions, R. Temam, and S. H. Wang, “New formulations of the primitive equations of atmosphere and applications,” Nonlinearity, vol. 5, no. 2, pp. 237-288, 1992. · Zbl 0746.76019 [6] J.-L. Lions, R. Temam, and S. H. Wang, “On the equations of the large-scale ocean,” Nonlinearity, vol. 5, no. 5, pp. 1007-1053, 1992. · Zbl 0766.35039 [7] J.-L. Lions, R. Temam, and S. Wang, “Models for the coupled atmosphere and ocean. (CAO I,II),” Computational Mechanics Advances, vol. 1, no. 1, pp. 5-54, 1993. · Zbl 0805.76011 [8] H. Luo, “Global solution of atmospheric circulation equations with humidity effect,” submitted. · Zbl 1246.86012 [9] C. Foia\cs and R. Temam, “Structure of the set of stationary solutions of the Navier-Stokes equations,” Communications on Pure and Applied Mathematics, vol. 30, no. 2, pp. 149-164, 1977. · Zbl 0335.35077 [10] L. Guazzotto and R. Betti, “Vlasov-maxwell equilibrium solutions for harris sheet magnetic field with kappa velocity distribution,” Physics of Plasmas, vol. 12, no. 7, pp. 56-107, 2005. [11] Y. G. Gu and W. J. Sun, “Nontrivial equilibrium solutions for a semilinear reaction-diffusion system,” Applied Mathematics and Mechanics, vol. 25, no. 12, pp. 1382-1389, 2004. · Zbl 1142.35469 [12] K. Liu and W. Liu, “Existence of equilibrium solutions to a size-structured predator-prey system with functional response,” Wuhan University Journal of Natural Sciences, vol. 14, no. 5, pp. 383-387, 2009. · Zbl 1206.92063 [13] L. C. Evans, Partial Differential Equations, vol. 19, American Mathematical Society, Providence, RI, USA, 1998. · Zbl 1080.81570 [14] R. Temam, Navier-Stokes Equations and Nonlinear Functional Analysis, vol. 41, SIAM, Philadelphia, Pa, USA, 1983. · Zbl 0522.35002 [15] R. Temam, Navier-Stokes Equations: Theory and Numerical Analysis, vol. 2, North-Holland Publishing Co., Amsterdam, The Netherlands, 1979. · Zbl 0426.35003 [16] T. Ma and S. H. Wang, Stability and Bifurcation of Nonlinear Evolution Equations, Science Press, Beijing, China, 2007. · Zbl 1298.35003 [17] T. Ma and S. Wang, Bifurcation Theory and Applications, vol. 53 of World Scientific Series on Nonlinear Science. Series A, World Scientific, Singapore, 2005. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.